dumb question- where is the oil filter housing on a cooper 's'?

 

It's under the hood, not underneath. Look behind the engine on the passenger side and you will see a large (36MM, IIRC) nut that is attached to a canister. The filter is in there.

 

This is the top view as you look into the engine bay



It's to the left of the exhaust shield at the back of the block.

Change oil when warm, and you'll find the threading much easier putting the filter can back on to the block.

But use a glove as it's hot!

Chris.